Neural Field Bumps & Traveling Waves
Wilson-Cowan continuum field theory — ∂u/∂t = −u + w★f(u) + I
Mode: Bump | Activity: —
The Wilson-Cowan neural field equation describes a continuum of neurons. The Mexican-hat connectivity kernel w(x) — excitatory center, inhibitory surround — supports localized activity bumps (working memory), traveling waves (seizures, sleep oscillations), and global oscillations. The firing rate function f(u) = 1/(1+exp(−(u−θ)/0.1)) is a sigmoid. Convolution is computed via direct summation on a 1D ring.